1. Field of the Invention
The present invention relates generally to measurement systems and more particularly to strain measurement systems.
2. Description of the Related Art
Coefficient of thermal expansion (CTE) is the fractional increase in size of a member per unit rise in temperature. If the member increases in length from an initial length L.sub.i to a final length L.sub.f when its temperature is raised by .theta. units of temperature, the coefficient of thermal expansion .alpha. is related to these parameters by the expression of L.sub.f =L.sub.i (1+.alpha..theta.). This expression can be rearranged to define .alpha. as ##EQU1## in which .DELTA.L is a differential length given by L.sub.f -L.sub.i and .epsilon. is the thermal strain .DELTA.L/L.sub.i which is induced in the member by the temperature rise. As shown by equation (1), the measurement of CTE involves the measurement of strain and differential temperature. Thus, any system which measures strain can be adapted for the more specific measurement of CTE.
Conventional techniques for measuring CTE include dilatometry and interferometry. In dilatometry, the expansion of a test member is compared to the expansion of a reference member whose CTE is either known or is negligible relative to the CTE of the test member. Rather than measuring the initial and final lengths (L.sub.i and L.sub.f) of the test member, dilatometry measures the difference in length .delta.L between the test member and the reference member. Because .delta.L is generally much less than L.sub.i and L.sub.f, the measurement accuracy is enhanced. Error sources in dilatometry include an imperfect knowledge of the reference member's CTE and inadvertent temperature differences between the test member and the reference member.
In interferometry, the expansion of a test member is measured relative to the wavelength of monochromatic light. A monochromatic light beam is split into first and second signals which are directed along first and second optical paths before being recombined. The optical paths are configured to include reflection from opposite ends of the test member. The difference in the optical path lengths causes a phase difference in the first and second signals which affects the amplitude of the recombined signal.
Expansion of the test member causes the first and second optical path lengths to change and this change is reflected in a change in the amplitude of the recombined signal. The measurement accuracy can be on the order of the radiation wavelength which is generally small, e.g., .about.1 micron for visible light. Interferometry measurement systems are typically complex and expensive. Error sources include the temperature sensitivities of optical equipment (e.g., lenses and retroreflectors) which must be exposed to the test temperature.
Dilatometry and interferometry measurement techniques are best suited for the measurement of homogeneous test members which expand linearly. Because their constituent parts may have different CTEs, composite members often bend or twist as they expand. Conventional dilatometry and interferometry techniques are typically not configured to correct for this complex expansion.
Exemplary composite members which are subjected to thermal stress are the solar wings 22 and 24 of the satellite 20 of FIG. 1. The satellite has a body 26 which carries various communication antennas, e.g., dish antennas 28, 29 and 30 and an array antenna 31. The solar wings 22 and 24 extend in opposite directions from the body 26 and they each carry a plurality of solar cells 32 on one wing face.
The satellite 20 is typically maintained in an attitude which directs the antennas at the Earth. The solar cells 32 convert solar radiation 33 to electrical energy for operation of the systems of the spacecraft 20. Accordingly, the solar wings 22 and 24 are connected to the body 26 with gimbals 34 so that they can be rotated towards the sun in order to enhance the reception of the solar radiation 33.
The cross section of FIG. 2 shows that each solar wing is typically formed as a composite panel 40 which has dissimilar skins 42 and 44 on opposite sides of a core 46. In an exemplary panel 40, the core 46 is aluminum honeycomb and the lower skin 44 is formed of a sheet of graphite epoxy composite. The upper skin 42 includes another sheet 48 of a graphite epoxy composite which adjoins the core 46 and the solar cells 30 which are bonded to the sheet 48. The solar cells 30 are typically carried on silicon substrates and covered with clear glass covers and are arranged in an adjoining relationship. The solar cells 30 have an exemplary thickness of 0.5 millimeters and the panel 40 has an exemplary thickness of 40 millimeters.
Thus, the composite panel 40 is substantially an aluminum honeycomb core with one skin of graphite epoxy and an opposite skin of graphite epoxy paved with higher-expansion solar cells. As its orbits about the Earth take the satellite 20 into and out of the Earth's shadow, the solar wings 22 and 24 are subjected to cycles of heating by the solar radiation 33. Because the spaced skins 42 and 44 have different CTEs, the solar wings bend from a first spatial shape which is indicated by solid lines in FIG. 1 to a second spatial shape which is indicated by broken lines 50. This bending induces torques upon the satellite 20 which disturb its attitude. As the satellite 20 moves into and out of the Earth's shade, the bending occurs so suddenly that it has commonly been referred to as "solar snap". In low earth orbits, the induced torques of some solar panels can be sufficient to overwhelm the attitude control systems of the satellite.
Accordingly, it is important to measure the linear and bending deformations of the composite panel 20 to evaluate the torques that will be induced upon a satellite. Accurate knowledge of these deformations can be used to design panels with decreased deformation and/or to accurately predict the torques that will be required of the satellite's attitude control system.